Final answer:
The current through the resistor 6.00 seconds after the switch is closed in a series circuit with a resistor, uncharged capacitor, and EMF, is found using the formula for the charging of a capacitor in an RC circuit with known values for resistance, capacitance, EMF, and time.
Step-by-step explanation:
The student's question involves a circuit with a resistor, a capacitor, and a battery. The student is asked to calculate the current through the resistor 6.00 seconds after the switch is closed, in a case where the capacitor is initially uncharged and an EMF of 33.6 V is provided by the battery. To find the current, we can use the formula for the charging of a capacitor through a resistor in an RC circuit:
I(t) = \( \frac{\epsilon}{R} \cdot e^{-\frac{t}{RC}} \)
Where:
- \(I(t)\) is the current at time t,
- \(\epsilon\) is the EMF of the battery,
- R is the resistance,
- C is the capacitance, and
- t is the time after the switch is closed.
Plugging in the given values:
R = 100 k\Omega = 100,000 \Omega
C = 20.0 \mu F = 20.0 \cdot 10^{-6} F
\(\epsilon\) = 33.6 V
t = 6.00 s
The time constant is \(RC = 100,000 \Omega \cdot 20.0 \cdot 10^{-6} F = 2\) s, so:
I(6.00 s) = \( \frac{33.6}{100,000} \cdot e^{-\frac{6.00}{2}} \)
From here, the student can calculate the current at time t = 6.00 seconds using the exponential decay function to find the final answer.